POLARIMETRY of COOL GIANTS and SUPERGIANTS Hugo E

Home , Polarimetry

POLARIMETRY OF COOL GIANTS AND SUPERGIANTS Hugo E. Schwarz Mullard Space Science Laboratory, University College London, Holmbury St. Mary, Dorking, Surrey, RH5 6NT, U.K.

ABSTRACT

The polarimetry of cool, bright stars is reviewed, with the emphasis on observational work. The progress made in spectral and spatial resolution, wavelength coverage and sensitivity is discusseg Polarigenic models are considered and some theoretical ideas are discussed. Several interesting classes of object are treated in some detail and some suggestions for future work are made.

i. INTRODUCTION

Historically both the intensity and direction of arrival of the light that reaches us from the stars have been measured and analysed as a function of time and wavelength. Until recently, all these observations were made in the visible wavelength range; that is roughly between 4000A and 8000A. In this review I will consider mainly this wavelength band but also some infra-red measurements.

All the starlight collected contains not only intensity and directional information but also possesses a state of polarization. The latter has been ignored for most of the time during which astronomical observations have been made.

The first (theoretical) step towards the concept of intrinsic stellar polarization was taken by Chandrasekhar (1946, 1947) who published the solution of the radiative transfer equation in an illuminated plane parallel atmosphere with Rayleigh scattering. This model predicts polarization effects in certain binary systems and in early-type single stars if a significant departure from LTE, that is a radiative asymmetry, is present. This is in fact the effect that Hall (1949) and Hiltner (1949) were looking for when they serendipitously discovered interstellar polarization (ISP).

Through the subsequent study of the wavelength dependence of the ISP, many of the properties of the interstellar medium have been determined. For instance much has been learned about the size distribution and chemical composition of interstellar dust.

Another well-studied feature of the interstellar medium is the structure of the Galactic magnetic field. Aligned polarization vectors trace the field lines through the paramagnetic grain alignment mechanism of Davis and Greenstein (1951).

In the decades after Hall and Hiltner's discovery it was found that some stars showed time variability in their polarization and a wavelength dependence unlike that generally observed for the ISP. It was realised that these stars were intrinsically polarized. The study of

J~vA 29:3-B 253 254 H.E. Schwarz

this intrinsic polarization which only certain groups of stars show, forms an important part of astronomical polarimetry and has contributed greatly to the rapid growth of this field in the past twenty years or so *.

Since the degree of intrinsic polarization of starlight is usually of order one percent or less, the original method of measurement, using photographic plates, could only be applied to a small number of highly polarized stars. The lower limit to the degree of polarization, p, which can be detected photographically is 5 to 10%, while modern photoelectric devices can measure p to accuracies of about 10-3%.

The advantage of the photograph in being capable of recording many images simultaneously is now rivalled by the latest two-dimensional detectors such as the CCD, IPCS and the electronograph. Polarization maps of extended sources and complete spectra of point sources can now be obtained in one observation. However, most high precision measurements of individual stars are made using photomultiplier tubes; their advent has accelerated the development of more accurate photometric and polarimetrie instrumentation.

Advances in polarimetric optics have also contributed to this increase in measurement accuracy. For instance Serkowski (1974) and Tinbergen (1974) have described the various optimum combinations of optical elements such as half- and quarter-wave plates, superaehromats and efficient, wide band polarizers. Schemes to compensate automatically for sky background light polarization have been proposed by Serkowski (1974) and Metz (1979). The method used by Metz also removes the wavelength dependent rotation of the polarization angle, present in superachomatic half wave plates.

An era has now arrived in which polarimetry can be performed at high spectral and spatial resolution, using low noise detectors with high detective quantum efficiency. The models explaining the observed phenomena are more constrained and have to be better and more

complicated than ever before.

2. EARLY YEARS

There are several groups of stars that have been identified as showing intrinsic polarization: Be stars, RV Tauri and T Tauri stars, R CrB stars, FK Gom stars, novae, white dwarfs, cool long period variables and irregular variable stars, symbiotics, 6 Scu stars and Ap stars, IE stars and carbon stars. In this review I will discuss only the cool stars among these groups.

The presence of intrinsic (as opposed to interstellar) polarization is usually inferred from temporal variations or a peculiar wavelength dependence of the observed degree and angle of polarization. The particular form of these variations can then be used to investigate the mechanism responsible for the intrinsic polarization and hence to study the physics of star atmospheres and the cire%tmstellar environment.

Most of the earlier observations were made using broad passbands or with just one wide-band filter giving only crude wavelength resolution or none at all. Some of this work on cool stars is presented in papers by Capps and Dyck (1972); Co]me and Kruszewski (1968); Coyne and Shawl (1973); Dyek (1968); Dyck et el. (1971a); Dyck and Jennings (1971); Kruszewski et

*The number of abstracts in Astron. Astrophys. Abs. pertaining to polarimetry has increased by about 300% relative to the total number of abstracts over the period 1969 to 1984. Polarimetry of Cool Giants and Supergiants 255 al. (1968); Serkowski (1971a) and zappala (1967). Important papers are also DombrovskiJ (1970); Dyek, et al. (1971b,c); Dyek and Sandford (1971); Serkowski (1966a, 1966b, 1969a, 1969b, 1970, 1971b); Shakhovskoj (1964); Shawl (1969, 1972), and Shawl and Zellner (1970).

These broad-band observations generally show that the polarization of most cool, bright stars decreases with wavelength and that variations with time of both the degree and angle of polarization are present. The form of the wavelength dependence can also vary with time: regularly for some stars, seemingly at random for others, with time scales from days to several years. Outbursts are sometimes also observed, for instance in symbiotics.

The groups of cool stars generally show an infra-red excess at ll~m which has been ascribed to eircumstellar silicate grains by Woolf and Ney (1969). Evidence of a correlation between this IR excess and the degree of polarization has been presented by Dyck et al. (19715).

Their graph of the degree of polarization, p, against the flux ratio at ll~m and 3.5~m is reproduced in Figure i.

• M STARS • CARBON STARS • S STARS

Figure i. Average degree of polarization versus the flux ratio at ii #m and 3.5 ~m (from Dyck et al. 19715).

el, •

f ] [ IOx I0 -2 20 X I0"2 30xJO -z 40xlO "z FX (l'ly.m) / F),.(5.5p.m)

Scattering in an asymmetrical grain distribution surrounding the star has been suggested as a possible mechanism to produce the observed polarizations.

Correlations of the degree of polarization with fundamental stellar parameters form an important area of study and some striking correlations have been found, especially with light curves and spectral type. For instance Dyek (1968) obtained observations of Mira-type variables which showed a decrease in the polarization with increasing visuallight. Kruszewski et al. (1968), whose diagram is reproduced in Figure 2, reported a maximum in the degree of polarization at minimum light for V CVn, a cool, irregular supergiant.

However, these correlations are not found in all stars. Zappala (1967) reported that he found no simple correlation between the polarization and brightness of a sample of Mira-type variables. 256 H.E. Schwarz

i ~ L i I I I I I I 6.5 @@ 7.0 v 7.5 ,,% ~o 8.o

8.5

8 o oo 6 oo N 8o Figure 2. V band light curve, degree P% 4 and angle of polarization for V CVn °%° (from Kruszewski et al., 1968). 2

110 o0OO 8 ° ;... . ~ , 100 I I i i I i I I I 2430200 2430300 J.D.

Large variations and strong correlations have been found for some individual stars and Shawl (1974) combined all the then available data on Mira in a folded (six cycles) diagram, reproduced in Figure 3.

i I I i r [ E

%% 4

2 1 Figure 3. U band polarization versus A phase for Mira (from Shawl, 1974). 0 T OOA•% I O Z~ O

O O I I r E ; i i O0 02 04 06 08 I0 12 PHASE

Clearly, a periodic modulation of the degree of polarization is present which is correlated with the stars light curve in the sense that maximum light coincides with (near) maximum polarization. These variations were ascribed to changes in a cloud surrounding the star, made up of dust and grains in a mixture which varies its composition with the phase of Mira. Note that the sense of the correlation between lightcurve and degree of polarization for Miras is opposite to that found by Dyck (1968).

Kruszewski et al. (1968) observed several cool stars and found changes with time in both the degree and angle of polarization which for some well-observed stars were correlated with their light curves. They also found that carbon stars, unlike M-type stars, have a flat wavelength dependence in the yellow-blue region. M-types tend to have a polarization which decreases monotonically towards longer wavelengths over the visible range. This generally observed decrease of p with wavelength indicates the possible presence of Rayleigh or dust scattering. A mixture of particles with scattering proportional to A -4 and A -I would produce, at least qualitatively, the correct wavelength dependence.

The influence of a region containing cireumstellar matter on the light curve and the polarization is important the observations have shown that regular variables exhibit Polarimetry of Cool Giants and Supergiants 257

straightforward correlations between polarization and light changes, while irregular stars do not. Mira variables could produce phase related changes in their circumstellar environment, for instance by periodically expelling dust shells which in turn will influence the observed polarization. Irregular variable stars might not show such mass loss behaviour and hence the polarization signature is not clearly linked to the stars light curve or to its spectral type variations.

Correlations between the intrinsic polarization of cool stars and Ca H and K emission line intensities have been reported by Dyck and Johnson (1969). Jefferies and Thomas (1959) and Athay and Skumanich (1968) associate the Ca H and K emission with a "hot" chromosphere which in turn is connected with a temperature inversion layer or a convective zone in the star. It is plausible that the presence of a convective zone wo~id give rise to major departures from LTE (Schwarzschild, 1975) and hence could produce significant polarizations as a result of the asymmetrical radiation field.

Dyck and Johnson (1969) plot the average nightly deviations of the observed polarization (i.e. a measure of intrinsic polarization as opposed to ISP, which should not vary with time) against the Ca H and K emission intensity using the scale of Wilson'and Bappu (1957). Their data are reproduced in Figure 4.

0.7

0.6

0.5 A% 0.4 Figure 4. Plot of average nightly deviation (A) of measured polarization versus Ca II K2 intensity (from Dyck and 0.S Johnson, 1969).

0.2

! 0.I |

mi__

INTENSITY

They conclude that stars with emission cores are generally unpolarized which seems to contradict the non-LTE argument above. Later data on some of the stars observed by Dyck and Johnson show that, for instance in the case of = Ori (Tinbergen et al., 1981) the deviations are much larger and the sense of their plot is in fact reversed by including several such observations. More observations need to Me investigated in this manner to resolve the question of polarization correlations with Ca H and K emission intensity.

The loci of polarized and unpolarized stars in the H-R diagram has been investigated by Dyck and Jennings (1971). Their diagram is reproduced in Figure 5. 258 H.E. Schwarz

-I0

-8

-6 o • o o O o -4

Mv ace Figure 5. Loci of polarized (o) and -2 unpolarized stars (e) in the HR-diagram (from Dyck and Jennings, 1971). • I,• e • o 0

4 i i KI4 ~ ~ ~ i r KO K2 MO M2 M4 M6 M8 SPECTRAL TYPE

It can he seen that K and M type supergiants are generally polarized but that only those giants cooler than about M4 tend to be polarized. Further, since the correlation between IK excess and polarization is a strong one (Dyck et al., 1971b) and the IR excess is ascribed to a circumstellar shell by Woolf and Ney (1969), Dyck and Jennings conclude that the region

producing the polarization also produces the IR excess. This implies that the source of polarization is circumstellar rather than photospheric in origin. The smooth dependence on wavelength of the polarization is assumed to preclude the influence of atmospheric opacity, which for the stars under consideration means that the Tie bands have no effect on the polarization. Again, later observations (e.g. Landstreet and Angel,1977; Clarke and Schwarz,1984) have shown that this is not the case; strong effects are observed across Tie

bands as well as several other molecular features. These are just some examples were high resolution spectropolarimetry has settled a controversial issue.

Other groups of stars do not show any significant systematic distribution in the HR-diagram as regards polarization. As an example I reproduce the data of Bastien (1985) in Figure 6. This sample of T Tauri stars forms a scatter plot in the HR-diagram and no correlation between polarization and locus seems to be present.

1.80 , o

1,00

1.20 ° =

0,80 = x ° |

Figure 6. HR diagram for T Tauri stars be x o = (open circles) p < 0.5%; (filled 0.00 " ~ ~ "~ circles) 1.2% < p < 2.0% and (triangles p > 2%) (from Bastien, 1985).

""~°3.0o 3'.,0 3.oo ;.~0 3.40 Log Teff Polarimetry of Cool Giants and Supergiants 259

3. POLARIGENIC MECHANISMS I

Mechanisms for producing the observed polarizations have been discussed by various workers who mainly considered four types: synchrotron emission, photospheric gas scattering, circumstellar gas or solid particle scattering. All mechanisms must have some underlying asymmetry to be able to produce a nett polarization in the integrated star light.

The synchrotron emission mechanism was considered unlikely by Shakhovskoj (1964) on the basis of radio and visual continuum distributions and also by Kruszewski et al., (1968) who argued that the spectral index if similar to that of known synchrotron emitters, would give a steeper wavelength dependence for the polarization than that observed.

The discussion of the remaining mechanisms is presented very clearly by Shawl (1974). Part of his review is as follows:

"Scattering from neutral hydrogen in an asymmetric cloud was suggested by Shakhovskoj (1964) as an explanation for the observed polarization t However models were not available until Kruszewski, Gehrels and Serkowski (1968) made calculations to find the maximum polarization possible from a circumstellar shell; they found a maximum polarization of 5.5% for Rayleigh scattering from H 2, with lower values for dielectric and metallic particles. Small dielectric particles were found to give a polarization approaching the 5.5% maximum. However they reported some stars with polarization greater than 5.5%. Therefore Harrington (1969) proposed that a polarization higher than 5.5% could he obtained if the polarization were caused by scattering in a photosphere that has a source function that varies strongly with optical depth, has appreciable absorption, and has a temperature variation of several hundred degrees between the pole and the equator. Harrington pointed out that this model predicts a variation of the polarization across spectral absorption features. Although this prediction has not been truly tested, Dyek and Sandford (1971) and Dyck and Jennings (1971) ruled out Harrington's photospheric model on the grounds that the TiO bands in late-type stars should cause a change in the wavelength dependence of polarization as one considers Stars of later spectral types; no such change was found by them.

Serkowski (1971b) on the other hand, believes that the UBV spectral regions are too wide to detect the effects of TiO bands on the wavelength dependence even if the effects are large. However, since TiO has a large effect on UBV photometry (Smak, 1964), it should likewise affect the polarization. Also, because of the IR excess, solid circumstellar material is known to exist around these stars. Therefore, it is likely that the polarization is primarily circumstellar rather than photospheric in origin.

Is the polarization caused by scattering from gas or from solid particles? As evidence against molecular scattering, Dyck and Jennings (1971) pointed out that some stars (7 Gem, ~ Aur, and ~ Her) show evidence of gas in a circumstellar cloud hut no polarization nor IR excess, and that it is unlikely that particles that absorb (to produce the ll~m excess) would also scatter". 260 H.E. Schwarz

As mentioned above, the argument about the presence of spectral polarimetrlc structure has now been settled and in this paper observational data is presented which clearly shows strong effects on both the degree and angle of polarization, especially across TiO bands. The presence of TiO related effects is evidence for a scattering process which takes place either below or in the TiO formation region, since circumstellar scattering alone cannot produce changes in the angle of polarization across these molecular features. The discussion about polarigenlc mechanisms is by no means settled and is still actively pursued by polarimetrlsts.

4. THE LAST DECADE

The book "Planets, Stars and Nebulae studied with Photopolarlmetry" edited by T. Gehrels (1974), based on IAU Colloquium 23 held in 1972, from which Shawl's quote has been taken, forms a milestone in the polarimetrle literature. It is in fact the only comprehensive review to date and is sometimes irreverently referred to as "The Polarimetric Bible". Also, perhaps by chance, it stands on the border of two eras in polarimetry which can be identified with early, often pioneering work and "modern" work, more accurate and with a dramatic increase in spectral and positional resolution and wavelength covered. Superachromatie wave plates and efficient polarizing prisms combined with narrow band filters or gratings/grisms and highly efficient detectors such as CCDs are responsible for this change in recent years.

Below a review of this post-1974 period is given, in which some emphasis has been given to three well studied objects: ~ Ori, VY CMa and R Aqr. The reason for this emphasis is the availability of high resolution polarlzation,spectra for these objects and the interesting spectral features which have been observed in them.

After 1974 it was found (Kruszewski and Coyne, 1976; McCall and Hough 1980) that some very cool stars such as VY CMa, NML Cyg and IRC 10216 showed unusually high degrees of polarization. Values of up to 25% for the central objects and 46% for the jet in VY CMa system have been measured (e.g. Serkowski, 1969a). The underlying mechanism producing these high polarizations was thought to be either an asymmetric envelope containing grains or extinction by non-spherlcal, aliEned particles, where neither possibility is without problems. Either the eircumstellar asymmetry or the alignment has to be explained.

For these more exotic IR objects, the interpretation of the observed correlation between (I-K) colour and polarization is also a controversial issue. Khozov et el. (1978) claim a strong correlation while Kruszewski and Coyne (1976) find "little correlation". Their plots are reproduced in Figures 7 and 8 respectively.

Khozov et al. conclude that there is one universal mechanism responsible for the polarizations produced in late-type stars but Krnszewski and Co)me do not present an argument for any specific mechanism. It does, however, seem clear from the results presented here that a correlation between IR eolour and polarization exists.

With the development of modern polarimeters the whole wavelength range from 3000A to I1000A has now been covered at medium to high resolution and several new features in the polarizations of cool stars have been discovered. The rapid change in the degree and angle of polarization across certain spectral features has now been well established for some stars, especially Mira-type variables (Boyle et ai.,1985; Coyne and McLean, 1979; McLean, 1979; McLean and Clarke, 1977). Polarimetry of Cool Giants and Supergiants 261

22 IRC 10215 •

20 IRC 10218 •

14 pI % NML Cyg

12 I ] I l I I I ~5 10 ®~ NML Cyg B • CIT 6

6 • CIT 6 IVYCMa 4 SP e :C~y:. u Cle'rCIT-13

2 RUHer MWHer% % ~ NML Tau e • • • UHere~- RUHer IT-5 RTCy~ Cyi CIT-5 0 ~-ell ml I Oo i ° i.:.;!"~ • I I I xcy~ I u I I I I I 0 1 2 3 4 5 6 7 8 9 2 ~ 4 5 6 7 8 I-K I-K

Figure 7. I band polarization versus Figure 8. Polarization versus I-K I-K colour (from Khozov et al., 1978). colour. High polarizations all have high values of I-K (from Kruszewski and Coyne, 1979).

9 £

R eoo c AA.. 40A ~Ae = 80A

z ,

e r ii

g,o

A;% ~ 8oA

' I I I , I , I l r I i I , I i i I 3•100 5000 ?000 9000 11000 3000 5000 7000 9000 11000

WAVELENGTH (A)

Figure 9. Angle (upper) and degree (centre) of polarization and intensity (lower) versus wavelength for U Her and E Boo (from Landstreet and Angel, 1977). 262 H.E. Schwarz

Figure 9 shows two examples of this kind of data, taken from Landstreet and Angel (1977) and obtained with a multichannel spectrophotometer converted to a polarimeter (Angel and Landstreet, 1974); these Mira-type variables show changes in the degree and angle of polarization. On the basis of these observations atmospheric features in the stars d_~ohave a strong influence on the polarization as can also be seen from the fact that in R And (Figure i0; also from Landstreet and Angel) the heavily blanketed part of the spectrum between 5500A and 7000A corresponds to an increase in the degree and (less clearly so) the angle of polarization.

The wavelength dependence also changes with time for these stars. Note the difference between the plots of Figure i0 and Figure ii. The observations presented in Figure ii are from Boyle et ai.1985 and show R And at a later date, at phase 0.06.

, , , J

~leo 14o I=o

R An~ (m~)

Ax ~. ,40 A AXe "160A R And

p(%)

AA~-160A 9 (o) 85

i i , i , , t , , 30100 45 I~000 4000 4500 5000 5500 WAVELENGTH ( A ) Wavelength (A)

Figure i0 As Figure 9 but for R And. Figure ii. Intensity (I), degree (p) and angle (8) of polarization as a function of wavelength for R And (from Boyle et al., 1985).

Note that the observations of Landstreet and Angel were made at phase 0.96, close to that of Boyle et al.. The polarimetric data, however, show major differences; the polarization angle has changed by about 65 ° at 4000A and its wavelength dependence has become flat, while the general level of polarization has changed from 0.5% to about 2%. Clearly, there are dramatic variations present which are either independent of the phase of the star or are related to the slope of the light curve; differences could exists between the rising and

falling part of the cycle which might be related to the behaviour of shock w~ves as they pass through the stellar atmosphere. Polarimetry of Cool Giants and Supergiants 263

Resolved spectral features also show polarimetrlc effects. For example the Balmer H E line (McLean and Coyne, 1978; McLean, 1979; Tomaszewski et al., 1980) and the Ca 4227A line (Boyle et ai.,1985) are associated with peaks in the degree of polarization and changes in position angle. Note that there are differences between the polarization changes across the Balmer emission lines and the Ca I absorption line in the spectrum of Figure ii. These effects do not seem to occur in irregular or semi-regular variables but only in regular pulsators such as Miras or in systems containing such variables, for instance symbiotic stars.

Of the irregular Variables, ~ Ori is the best studied star for polarimetry. Several workers have presented observations: Behr (1959), Capps and Dyck (1972), Clarke and Schwarz (1984), Dyck (1968), Dyck et al., (1971b), Dyck and Jennings (1971), Hayes (1980, 1981, 1984),

Kruszewski and Coy'he (1976), Serkowski (1971b) and Tinbergen, Greenberg and de Jager (1981) (TGJ from here on).

As mentioned above, the earlier observations showed that the polarization varies with time, decreases with wavelength, and is small (typically less than one percent). The more recent observations show significant polarization changes across TiO bands. In Figures 12 and 13 the measurements of TGJ and Hayes (1984) are reproduced respectively.

8 7 6 5 ~ 3 2 Possbor~ 1

Ori d

,~ ' 2'o ' 3'o ¢ x'

Figure 12. Degree of polarization of ~ Orionis for several epochs ( a-e) plotted as a function of wavelength (from Tinbergen et al., 1981).

The data show time variations which are significant over periods of less than two months. Also, in TGJ's measures there seems to be a feature common to all data runs at TiO 6651A which could be an unresolved dip in the polarization across this molecular absorption band. A re-analysls of TGJ's data has shown (Schwarz, 1984) that there is indeed a feature present in both the degree and angle of polarization. In the high resolution data of Clarke and Schwarz, reproduced in Figure 14, there are significant dips in the polarization as well as peaks in the angle of vibration across all major TiO bands and similar effects are present in a set of observations of VY CMa (Aspin, et al., 1985a) which are reproduced in Figure 15.

These results could be indicative of a single mechanism, present in two objects as different as ~ Ori and VY CMa, being responsible for the polarizations. This could be added to the statement made by Khozov et al. (1978) concerning a universal mechanism being responsible for the polarization in a wide range of objects, varying from "normal" irregular stars of the cooler spectral types to exotic infra red objects. All these polarimetric observations of ~ Orionis combined with the light curve, the radial velocity and spectral variations (see e.g. Weymann, 1962) support the idea of the existence of large convection cells in the 264 H.E. Schwarz

star's photosphere as investigated theoretically and suggested as a possible polarigenic mechanism by Schwarzschild (1975). A detailed discussion of these hotspots or convection cells as the underlying mechanism responsible for the polarization of (super)giant stars is presented below.

~ 0.9 .... I ...... t--' ' " ...... I ...... I .... 0.8 Z o

I / ]60 /// 140 iii/ Z ~_ 120 < N I00 rr 5 ao 0 60 0 w 4°i .J ~ 20

< 0 I I i i i i i t i i i I I I i i i i i i i i i i i i i i 7:7 NOd FMAMIJ9:0ASONDI d FMAMI;:IASOND J FMAMI~:2ASONDJ F19:3M

Figure 13. Degree and angle of polarization of ~ Ori as a function of time (after Hayes, 1984).

A more exotic possibility for the origin of the polarization of ~ Ori has recently been proposed by Karovska (1985). A close (0".06) companion orbits ~ Ori and produces a regular variation in the polarization of the system with a period of -2.1 years. Speckle interferometry, photometry and radial velocity data are all used to support Karovska's argument. It is interesting to note here that there could be a 27 month periodicity in Hayes (1984) data, shown in Figure 8. The maxima at 2/81 and 5/83 and the minima at 8/80 and 11/82 define a curve with a shape not unlike that of a Mira variable light curve. More time coverage is clearly needed to enable an unambiguous determination of this periodicity to be made. Polarimetry of Cool Giants and Supergiants 265

~10c

r- (a) a c

5C O Figure 14. I, p and 8 versus wavelength for ~ Ori. Note strong effects across x 30 Ti O absorption bands (from Clarke and o- Schwarz, 1984). io

t25 - ia errr o (~ 12o

,,5 c: 0 (c) C ~to O .l 105

i l i i

1.0

"~ O.B

"~ 0.6 v >- I- 0.4 Z Id ~- O.Z z

Figure 15. !, P and B versus wavelength for VY CMa. Again, strong effects n.0 across spectral features are present Z (from Aspin et al., 1985a). 0 I0,0 < n~ 9,0 < J n0 8.0

o3 uJ

140 < Z o

130 n

4000 45OO 50OO 5500

WAVELENGTH (~) 266 H.E. Schwarz

5. POLARIGENIC MECHANISMS II

In addition to a scattering region the presence of some asymmetry is needed to produce a nett polarization when observing the spatially integrated light from a star.

Several mechanisms to generate asymmetries have been proposed. A pole to equator temperature gradient with photospheric scattering (Harrington, 1969), non-radlal pulsations (e.g. Cox, 1976), non-spherlcally symmetrical circumstellar envelopes (Dyck et al., 1971c) and large convection cells or hotspots (Schwarzschild, 1975).

By considering typical observed tlmescales of polarization changes in cool giants and supergiants (> i month) and estimating the timescale of these proposed mechanisms, (-4 years) Schwarz and Clarke (1984) have shown that convection cells are the only mechanism which is not a priorl discountable by the observations on the basis of time scale arguments.

By using a simple model with two convection cells and electron scattering Schwarz and Clarke have shown that all the observed polarimetric features in ~ Orionis can be reproduced by this model. The strong and peculiar wavelength dependence observed (see Figure 14) is mimicked by the model star when limb darkening is included; a typical data set produced by the model is shown in Figure 16.

5'O A

2'5

o o.o

5o"

c'- ._o

°~ Figure 16. I, p and 6 versus wavelength for a model star (see text) (from Clarke no and Schwarz, 1984).

"~ - O. n0 ~ i i i i 5000 6000 7000 8000 xl,&) Only Thomson scattering was considered both for simplicity and to show that because of differences between the emissivities of the spots and the general photosphere, the hotspot model produces an intrinsic wavelength dependence llke that observed, without having a scattering mechanism with its own wavelength dependence. The overall gradual change in the degree and angle of polarization is produced by the same differing Spectral dependencies of the photosphere and the hotspots, while the Strong effects across spectral features are caused by a dlfferentlal llmb darkening coefficient (see de Jager, 1981). The posslble depolarization due to reprocesslng in the high opacity TiO bands could als0 contribute to the variations across such spectral features. Polarimetry of Cool Giants and Supergiants 267

To date this seems to be the only model in which the underlying polarigenic mechanism is considered rather than just the properties of the scattering region.

Recently, Doherty (1985) has taken the model of Schwarz and Clarke and included a more realistic scattering atmosphere as well as limb darkening. He considered that the electron density required to produce the observed levels of polarization is too high and suggests Rayleigh scattering to explain the observations. His results combine for the first time the underlying asymmetry and a more detailed scattering process.

The typical changes in degree and angle of polarization across TiO bands have been observed in widely differing stars. For example in ~ Orlonis by Clarke and Schwarz (1984), in Mira variables by Landstreet and Angel (1977), in VY CMa by Aspin et al. (1985a) and in R Aqr by Aspin et al. (1985b). It is therefore possible that these convection cells are present in a variety of massive cool stars together with different scattering regions whose properties depend on the type of object and determine the overall observed polarimetric behaviour.

The properties of the polarization of scattered light produced in circumstellar envelopes has been treated by Brown and McLean (1977). The considered axisymmetriic envelopes with Thomson or Raylelgh scattering only. Simmons (1982) derived analytical expressions for the wavelength behavlour of the polarization from arbitrary scattering mechanisms in optically thin single star envelopes and extended this work to binary systems in a subsequent paper (Simmons, 1983). These theoretical expressions could be combined with the above asymmetries, introduced by convectlon~cells, to produce absolute values for the degree of polarization as a function of wavelength for extended stellar envelopes.

6. OBSERVATIONS OF DIFFERENT GROUPS OF STARS

6.1 Irregular and seml-regular variables

This group of cool giants and supergiants has been well studied polarimetrically. The observed polarizations are low, typically 1% or less, the degree and angle of polarization both vary irregularly with time (e.g. Hayes, 1984) and the wavelength dependence which generally gives a polarization decreasing towards longer wavelengths, also varies with time (e.g. Shawl, 1972 and TGJ). Observations have also been presented by Polyakova, (1978, 1981, 1982, 1983), Arsenljevic et al. (1980) and Abramyan (1980, 1981).

Samples of these stars have been studied by various au£hors (see references in section 2) and more recently by Schwarz (1985) who showed that the average degree of polarization decreases from -0.6% for spectral type M3 to zero for type KO. Clarke et al. (1985) have presented results on several individual stars, some of which show narrow band effects across spectral features. One star (7 Per) shows the Stenflo (1979) resonant scattering effect in the Ca II K llne.

Red giants have been measured for polarimetry in the infra-red (Dyck and Lonsdale,1980; McCall and Hough, 1980) and have been observed by Whlte et al. (1984) to be intrinsically polarized up to 2% in two globular clusters.

6.2 Miras

Typical observed polarizations in Mira's vary between a few percent and nearly zero in a regular manner and the variations are correlated with the light curve. Figure 3 shows 6 polarimetric cycles of o Cet folded onto the phase of maximum light. Clearly, near maximum 268 H.E. Schwarz

light corresponds to maximum polarization. Several Mira's have been observed for polarization and data have been presented by: Boyle et al. (1985), Codina-Landaberry and Magalhaes, (1980), Coyne and McLean (1979), Coyne and Magalhaes, (1979), Dyck, (1968), Hayes, (1982), Hayes and Russo (1981), Kruszewskl et al. (1968), Landstreet and Angel (1977), McCall and Hough, (1980), McLean (1979), McLean and Clarke (1977), Magalhaes and Coyne, (1985), Svatos (1980), Svatos and Sole (1981a, b), Tomaszewski et al. (1980) and Zappala, (1967).

Shockwaves carrying dust shells expelled by the star in a regular manner have been invoked by several of the above authors to explain the observed polarizations. Alignment of the grains is unexplained and sufficient asymmetries are not easy to produce in these models. No model which satisfactorily explains the observed features has been presented to date and more work is clearly needed. (See also the section on symblotlcs and the discussion of the peculiar object E Aqr.)

High resolution polarization spectra for a sample of Mira variables have been presented recently by Boyle et al.19g5. Their data, part of which is reproduced in Figure 17, shows several interesting effects across spectral features.

I 0.5

2 p(%) 0.5 1

0 "Y 50 110

70 170

30 110 4000 4500 ,000 5500 4000 4500 5000 5500

Figure 17. I, p and # for O Cet and U Her against wavelength. Note the differences between these resDits for U Her and those of Figure 9 (from Boyle et al., 1985).

There is no general trend among the sample; many different phases are involved and among Miras, M, S and C-types have been observed. Several of the stars show polarization dips at Ca 4227A, changes across Balmer lines and [OIII] as well as strong effects across TiO bands. More stars need to he observed with this method and at several times to separate phase related effects from differences intrinsic to the star types.

It is also noted here that the polarimetry of Miras and irregular/seml-regular variables has been reviewed by Coyne and McLean (1979). They presented the high resolution measurements of Landstreet and Angel (1977) and McLean and Coyne (1978) and the observations made by Coyne and Magalhaes (1979), as well as a discussion of the various polarigenlc mechanisms under consideration at that time. The then recently discovered enhanced Balmer emission line polarizations in Miras, for instance, were ascribed to a shock wave moving through the atmosphere of the star, while Harrlngton's photospheric anisotropy model was favoured by Coyne and McLean to explain the continuum polarization in red variables in general. Polarimetry of Cool Giants and Supergiants 269

6.3 Symbiotics

Symbiotic stars have been known to exist for a long time. Their discovery by Merrill and Humason was as long ago as 1932 although Merrill (1958) was the first to use the term "symbiotic". Much work has been published in the fields of photometry, spectroscopy etc., but not until recently did the polarimetric study of these objects begin.

The polarimetry .of symbiotics started with the work of Shakhovskoj (1969) on R Aquarii, a bright and hence the best studied symbiotic. Serkowski (1970) made measurements of R Aqr, RS Oph and AG Peg and found variable polarization in all three objects albeit only at a marginal level for RS Oph. Observations of other symbiotics were made by Barbier and Swings (1982), Belokon and Shulov (1974), Efimov (1979) and Piirola (1982, 1983).

Recently, Schulte-Ladbeck (1985a) has published a polarimetrie survey of northern symblotlcs. She found that out of 18 (2 previously observed) stars, 8 showed intrinsic polarization. She discussed the distribution of intrinsic polarization among S and D types and found that 4 stars of each type were polarized. By spectral type, more of the later types showed polarization, as can be seen from Figure 18, taken from Schulte-Ladbeck's paper.

unpolorized I

Figure 18. Distribution among spectral types of polarized an~! unpolarized -- symbiotic stars. There is an indication polorized that only those of M4 or later type are polarized (from Schulte-Ladbeck, 1985a).

Clearly, the statistics of these observations can and need to be improved by observing a larger sample of stars and also by improving the detectivity of the observations. Lower values of polarization might be present and these could be of an intrinsic nature.

Time coverage of the intrinsic polarization is also of importance since many symbiotics contain a regularly varying cool star, often a Mira-type variable. A study of the interaction of the expelled dust shell from the Mira with the hot gas surrounding the system is then possible.

JPVA 2913-C 270 H.E. Schwarz

The detailed polarigenic mechanism for symbiotics is not well understood at present. Scattering in gas and dust surrounding the system is named as a likely cause of polarization but the underlying asymmetry is not explained. More work is needed urgently in this area of study.

An interesting symbiotic which shows occasional outbursts is AS338, observed polarimetrically by Schulte-Ladbeck (1985b). Svatos and Solc (1981b) observed R Aqr and on the basis of similarities between its polarization and that of o Cet suggested that R Aqr is a single star which shows flaring activity. The single star hypothesis for symbiotics is not generally accepted. The long period (44 years) of the R Aqr system is not explained by this model, but is by the binary model.

Recently, it has been shown that the polarimetrlc spectrum of R Aqr is very complicated. The data presented by Aspln et el. (1985b) show increases in p across TiO bands, effects across emission lines and a -40 ° swing in the angle of polarization over a 200A range, where the opacity suddenly changes. These observations are shown in Figure 19 as plots of the intensity, degree and angle of polarization versus wavelength.

R AQR 0"50 -1-=-" I .... :- ~ : ~ -' -- -! ...... ' ...... !

~515 ~]L/q/,I.,,,~v ,,~Ul,]/~/'lil~ .~/~V/ ~j ~ , k/ ~ , ,

-7.5

15 Figure 19. Log I, p and 8 spectra for R Aqr. Note the very complex structure in the p and 8 spectra and the sudden 5 absence of features in the degree of polarization above about 6400 A (from 0 Aspin et el., 1985b)

155

150 ® 1:35

120 4500 5000 5500 6000 6500 7000 7500 8000 8500 WAVELENGTH (~)

Observations of R Aqr made near maximum light (unpublished) show that the polarization can be as low as 0.5%, while this can be as high as 18% near minimum light (see Figure 19). Clearly, very drastic changes in the physical conditions in this system are needed to produce such large differences in the polarization.

The polarimetry of symbiotlcs is a relatively new area of study; there is only a small observational data base and many more observations are needed. A problem is the faintness of a high proportion of these stars, requiring time on large telescopes.

6.4 T Tauri stars

Polarimetric observations of T Tauri stars have been presented by ~astien (1979,1982,1985), Schulte-Ladbeck (1983) and by Solc and Svatos (1983).

The survey of northern T Tauris by Bastien (1982) has now been extended to the southern sky (Bastien,1985). Out of a total sample of 85 stars 13 show variable and therefore intrinsic polarization. Only about 30 stars were observed well enough to determine variability and Polarimetry of Cool Giants and Supergiants 271

more than one third of these were intrinsically polarized. Schulte-Ladbeck (1983) observed variable polarization in 6 stars and also obtained wavelength coverage. Most stars show a slight decrease in p with wavelength. This was also observed by Bastien for four stars.

Correlations between several stellar parameters and the degree of polarization were investigated by Bastien. The only correlations found by him were with IR excess, He I and [OI] equivalent widths. The polarization at 5900A versus IR excess is plotted in Figure 20. Clearly, the polarized stars all have high excesses.

lO ' ' ' ' I ' ' ' L I ' ' ' ' I ' ' i , HL Tau"

6 • DG Tau

.LHa 332-20 ,VW Cha 4 ,DO Tau • • • ,RY Tau 2 WWCha • , • • • 2V866 Sco HM7 .'" .~ • 22 : • " " .V1515 Cy, • , "FU Orl V380 Ori 0 -1.o 1.0 3.0 5.0 7.0 {--(V-L)o

Figure 20, Degree of polarization at 5900 A versus a measure of IR excess for a sample of T Tauri stars (from Bastien, 1985).

The possible mechanism for producing the polarization is discussed by Bastien and he concludes that circumstellar material or a reflection nebula are responsible. Schulte-Ladbeck notes that on the basis of the wavelength dependence of the polarization, a wide range of grain sizes must be present in the circumstellar material. Bastien found a strong one to one correlation for his sample between the degree of polarization at 5900A and at 7540A. This might indicate a narrow range of grain sizes in the scattering material. It is clear that more observations are needed to resolve these questions.

An interesting mechanism to produce the polarizations, suggested by Solc and Svatos, is the interaction of X- and UV radiation, pro&need in strong flares, with a silicate dust cloud surrounding the star. The high-energy photons erode the grains and the accompanying change in size changes their polarimetric properties.

6.5 VY Canis Majoris

The VY Canis Majoris system is of special interest because of its many, complex features and the uncertainty of the evolutionary status of its central star (HD8061). Either a massive pre-main sequence object or an old supergiant are consistent with the available data (Hyland et ai.,1969, Herbig,1970). The central star is embedded in a dense nebula (e.g. Perrine,1923) whose most prominent feature is a jet extending about i0" to the NW (H~rbig,1972). The system also is a strong infrared source (Neugebauer and Leighton,1969) and OH emitter (Eliasson and Bartlett,1969), indicating the presence of significant amounts of re-thermalising dust in the circumstellar environment. This object deserves discussion in some detail.

Several authors have presented polarimetric observations of VY CMa. These include broadband optical measures by Serkowski (1969b), Shawl (1969), Dyek et el. (1971a), Capps and Dyck (1972) and Hashimoto et el. (1970). Serkowski (1973) noted that polarimetric time variations of order 1% might be present. This interpretation was complicated, however, by 272 H.E. Schwarz

the fact that different sized apertures were used for the various observations. Thus, by including more or less of the highly polarized nebular light, differences in the measured polarization from one observation to the next could have been generated.

More recently, high wavelength resolution measurements made by Aspin et al. (1985a) showed that VY CMa possesses complicated structure in both the degree, p, and position angle, #, of polarization, especially across spectral features such as TiO bands. These observations were the first to be made with a small (2 x 4 arcsec 2) aperture accurately centered on the star. In this manner, nearly all of the nebular light was excluded and hence the polarization of the central object only was measured. The availability of measurements of the polarization of the central star, the star plus nebulosity and a single wavelength (4300~) measurement of the jet in isolation, has enabled the wavelength dependence of the jet polarization to be calculated.

Figure 21 shows the red data on VY CMa of Aspln et al. (1985a). By taking values at 5 wavelength points and taking the ratio of these with the existing broadband data the plot of Figure 22 is obtained.

~ .E

"~ 0.~

0.4 Z l.d 0.2 z

8.C Z 7.C I-- < N 6.0

< 5.Q .3 4.0 Q.0 4.0

3.0 hJ 140 Rp Z < 2.0 130 Z o I- 120 0 1.0

I I i0 I I 5700 6200 6700 7200 7700 8200 4000 60 0 8000

WAVELENGTH (A) X(A)

Figure 21. Red I, p and 8 spectra for Figure 22. Ratio of the polarization of VY CMa. Correlations in p and 8 with the whole VY CMa system and the central Ti O bands are again present (from Aspin star alone versus wavelength. Two et el., 1985a). polarigenic mechanisms are clearly present (from Schwarz and Aspin, 1985). Polarimetry of Cool Giants and Supergiants 273

This shows the ratio of the whole object polarization and the central object polarization. The ratio decreases monotonically from about 3 at 4000~ to unity at 8000~. This indicates the presence of more than one polarigenic mechanism for the following reason. Simple dilution of the stellar polarization by unpolarized nebular light would produce a ratio of less than unity. The jet must produce radiation with a higher degree of polarization than that of the star. Two polarigenic mechanisms are therefore present in the VY Canis Majoris system: one in the star and one in the jet. Further conclusions which can be drawn from the plot of Figure 22 are that the mechanism in the jet is more effective in producing polarization in the blue than in the red and that this wavelength dependence is steeper than that due to the mechanism operating in the central star. Thus it seems likely that Kayleigh scattering is responsible for the Jet polarization.

Assuming therefore that the jet polarization is caused by Rayleigh scattering, then in the absence of an additional light source in the aperture centred on the jet, a flat wavelength dependence of the polarization would result. This is due to the fact that both the polarized and unpolarized Rayleigh components vary as the inverse fourth power of the wavelength. Normalising to obtain the Stokes parameters then cancels out this wavelength dependence, resulting in a constant polarization value.

However, there are two other sources of radiation present in the aperture centred on the jet. One is the diffuse background contribution from star light which amounts to about 17.5 meg in the B band at the Galactic latitude of VY CMa (Allen, 1964) and the other is the scattered profile light of the star itself. A study of stellar profiles has been published by King (1971). Using his data to integrate over the 12" circular aperture gives -11.5 meg of scattered starlight in the B band. Clearly, the diffuse background light can be neglected in comparison with the profile light.

This profile radiation is added tO the intrinsically polarized light from the jet to produce the observed overall polarization of 43% at 4300~. To obtain the intrinsic jet polarization, this profile light contribution must be corrected for.

VY CMa has a brightness in the B band of about 9.5 meg (Serkowski,1969) and a profile light contribution of about 11.5 meg in the B band is present. In other words the profile radiation is about 16% of that of the star at 4300~.

By considering these data, we can find the observed brightness of the jet relative to that of the star. Using the Stokes parameters of the jet, central star and the combined (star + jet) value, a ratio of the jet and star brightness of -0.39 is obtained.

Now we have

IN - 0.39I@

Ip - 0.161@

where IN, I, and Ip are respectively the brightness of the jet plus profile, the star and the profile radiation.

The intrinsic jet polarization at 4300~ is therefore -73% and not 43% as measured. This follows from the factor IN/(IN - Ip) which corrects for the dilution of the jet polarization by the profile light. 274 H.E. Schwarz

Now the values of the jet polarization at the remaining wavelength points can be calculated. The jet polarization as would be observed, the star polarization and the star+jet values are plotted in Figure 23.

u (%) symbol X (~) -]0 o 4300 5200 v 6500 7500 8500

J | ,, 10 2% q¢Io, + @

Figure 23. Normallsed Stokes parameter plot of the jet (+ve U, open symbols), star (open symbols with bars), observed star + jet (filled symbols) and derived star + jet (open symbols) values. See text for an explanation of the derived values (from Schwarz and Aspin, 1985).

By multiplying these values by the dilution factor IN/(I N - IF) we obtain intrinsic jet polarization values as listed in Table i.

Table 1

A(~) Pintrinsic(%) Poverall(% ) Pln/i,(% ) 4300 73 43 17 5200 71 35 8 6500 73 23 3 7500 75 17 2 8500 73 ii 1

As predicted by the assumption of Rayleigh scattering in the jet, Pintrinsic is constant with wavelength to within the experimental Uncertainties. For completeness, the overall observed values of p and the values obtained after dilution by the total stellar light are also tabulated, where the stellar light is assumed to he unpolarized.

The values of piN/1, are plotted in Figure 23 and have been used together with the measurements of the central star to calculate the combined polarization data points of star plus nebula. These can be compared with the observed values and from Figure 23 it can be seen that a reasonable fit is obtained.

The wavelength dependence of the jet must now be studied observationally to test the assumptions made in this model. Polarimetry of Cool Giants and Supergiants 275

7. CONCLUSIONS AND FUTURE WORK

In recent years the dramatic increase in spectral and spatial resolution applied to polarimetry has produced large quantities of data on the behaviour of the degree and angle of polarization as a function of wavelength and position. Effects of enhanced or decreased polarization across spectral features such as Balmer and [OIII] emission lines, Ca I 4227, Ca II H and K absorption lines and molecular bands have been observed. Only partial explanations and models have been produced and further work in modelling these complex polarimetric phenomena is needed.

To obtain these spectra at regular intervals during the phase of Miras, symbiotics and semi-regular variables must be an observational priority. Some time coverage has been obtained, for instance for K Aqr (Serkowski, 1969a; Aspin et al., 1985b) and R And (Landstreet and Angel,1977; Boyle et al., 1985), but no comprehensive set of observations exists as yet.

To study general trends of polarimetric behaviour among stars, larger samples of objects within a class such as, say, Miras must be obse~rved. Blue polarimetry of carbon stars is also of importance for the modelling of these star atmospheres. Clearly, these observations are difficult to perform because of the extreme red nature of the spectra of these stars.

Symbiotics should also be surveyed polarimetrieally, a start with this work has been made by Piirola (1983) and Schulte-Ladbeek (1985a) but statistics on the distribution of intrinsic polarization among symbiotics are very poor at present.

With the availability of IRAS' infra-red spectra of a large number of cool stars, correlations between spectral features such as the ii ~m excess and the presence and degree of optical polarization can be investigated in detail, both as a function of phase for regular variables and from one class of object to another.

Finally, the simultaneous observations of the polarization, UBV photometry and imaging by speckle interferometry as initiated by Lynds et al. (1976) and more recently by Roddier and Roddier (1985) could give valuable clues as to the reality of the convection cell or hotspot model. The binary model of Karovska (1985) for ~ Orlonls could also be investigated with this method. The angle of polarization and the position angle of any observed asymmetrical feature could be correlated - the sense of the correlation can eliminate the usual model ambiguities.

It is impossible to predict what the future holds but cool star polarlmetry clearly has an important and interesting role to play in the continued growth of our understanding of these objects.

To conclude, the present situation as regards cool star studies is summed up beautifully in Figure 24, taken from Gustaffson (1981).

Acknowledgements

The author thanks Professor J.L. Culhane for his support and Dr.D. Clarke for critically reading the manuscript and suggesting several improvements. This work was supported by the SERC. 276 H, E. Schwarz

Figure 24. The state of classical theory under the onslaught of sophisticated observations (from Gustaffson, 1981).

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